FD1D_PREDATOR_PREY is a FORTRAN77 program which solves a predator-prey system in a one dimensional region.
The nondimensional problem has the form
du/dt = del u + ( 1 - u ) * u - v * h(u/alpha) dv/dt = delta * del v - gamma * v + beta * v * h(u/alpha)with initial conditions:
u(x,0) = u0(x) v(x,0) = v0(x)and boundary conditions at the left and right endpoints [A,B]:
du/dx = 0 dv/dx = 0The Type II functional response employed here is
h(eta) = eta / ( 1 + eta )The parameters ALPHA, BETA, GAMMA and DELTA are strictly positive.
The user must input a value H specifying the desired space step to be used in discretizing the space dimension.
A finite difference scheme is employed to integrate the problem from time 0 to a maximum time T. The user must input the value T, as well as an appropriate time step DELT.
Typical data for this problem is:
ALPHA = 0.3 BETA = 2.0 GAMMA = 0.8 DELTA = 1.0 A = 0.0 B = 200.0 H = 0.5 T = 40.0 DELT = 0.0104 GAUSS = 0 (0 = direct solution, 1 = Jacobi )with the initial values of U and V set, for instance, to:
u0(1:n) = exp ( - ( x(1:n) - 100.0 )**2 ) / 5.0 v0(1:n) = 2.0 / 5.0
FD1D_PREDATOR_PREY is available in a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.
FD1D_BURGERS_LAX, a FORTRAN77 program which applies the finite difference method and the Lax-Wendroff method to solve the non-viscous time-dependent Burgers equation in one spatial dimension.
FD1D_BURGERS_LEAP, a FORTRAN77 program which applies the finite difference method and the leapfrog approach to solve the non-viscous time-dependent Burgers equation in one spatial dimension.
FD1D_BVP, a FORTRAN77 program which applies the finite difference method to a two point boundary value problem in one spatial dimension.
FD1D_HEAT_EXPLICIT, a FORTRAN77 program which uses the finite difference method and explicit time stepping to solve the time dependent heat equation in 1D.
FD1D_HEAT_IMPLICIT, a FORTRAN77 program which uses the finite difference method and implicit time stepping to solve the time dependent heat equation in 1D.
FD1D_HEAT_STEADY, a FORTRAN77 program which uses the finite difference method to solve the steady (time independent) heat equation in 1D.
FD1D_PREDATOR_PREY_PLOT, a MATLAB program which displays the solution components computed by FD1D.
FD1D_WAVE, a FORTRAN77 program which applies the finite difference method to solve the time-dependent wave equation utt = c * uxx in one spatial dimension.
FD2D_PREDATOR_PREY, a FORTRAN90 program which implements a finite difference algorithm for a predator-prey system with spatial variation in 2D.
FEM1D, a FORTRAN90 program which applies the finite element method, with piecewise linear basis functions, to a two point boundary value problem;
You can go up one level to the FORTRAN77 source codes.